Preheat the oven to 220°. On a large sheet of foil, toss the beets whole with 1 tablespoon of the oil; season with salt and pepper and wrap up with the foil. Roast for about 45 minutes, until tender. Unwrap and let the beets cool, then peel. Cut into wedges and place in a bowl. Add the red wine vinegar and toss.
Meanwhile, in a medium saucepan, cover the quinoa with 2 cups of water and bring to the boil. Cover and cook over moderately low heat for about 15 minutes, until all the water is absorbed. Fluff the quinoa with a fork and transfer to a bowl to cool slightly. Add the lemon zest and 2 tablespoons of the lemon juice; season with salt and pepper.
In a bowl, smash the berries with a fork and add 1 tablespoon of the olive oil until a chunky sauce forms. Season with a little salt.
In a small bowl, mash the avocado with the remaining lemon juice; season with salt and pepper.
Spoon the quinoa into bowls. Arrange the beets on top and spoon the berry sauce over the beets. Dollop with the avocado, garnish with pistachios and serve.